*** Please answer B-F and explain the steps I already asked this question once**

Question

*** Please answer B-F and explain the steps I already asked this question once*****

A 23 kg package is hanging from a rope wrapped around a winch (a cylinder with a handle) as shown in this diagram. The cylinder has a mass of 5.5 kg and a radius of 0.22 meters. The handle is 0.12 m from   the axis of rotation and has a negligible mass. Imagine that you let go of the handle and the package starts to fall.

B) Write an equation that relates the acceleration of the package to the forces on the package.

C) Write an equation that relates the angular acceleration of the cylinder to the tension in the rope.

D) Write an equation that connects the linear acceleration of the package to the angular acceleration of the cylinder.

E) Combine these equations and calculate the linear acceleration of the package as it falls. (Hint: Should this answer be more or less than 9.8 m/s2?)

F) Assuming the rope is long enough, how long will it take for the package to fall 4.3 meters?

Explanation / Answer

(B) Fnet = m a

23g - T = 23 a

a = g - (T/23)

(C) net torque = I alpha

R T = ( M R^2 /2) alpha

alpha = 2 T / (5.5 R)

(D) alpha = a / R

(E) alpha = a / R = 2 T / 5.5 R

T = 5.5a/ 2 = 2.75a

putting in 1st equation,

23g - 2.75a = 23a

a = 8.75 m/s^2

(f) d = u t + a t^2 /2

4.3 = 0 + 8.75 t^2 /2

t = 1 sec

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